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Finding the Fourth Proportional to 1,109.53, 1,664.77 and 416.10

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Solution

The fourth proportional to 1,109.53, 1,664.77 and 416.10 is: 624.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,109.53 : 1,664.77 = 416.10 : x
  2. Step 2: Convert to fraction form
    1,109.53/1,664.77 = 416.10/x
  3. Step 3: Cross multiply
    1,109.53x = 1,664.77 × 416.10
  4. Step 4: Simplify right side
    1,109.53x = 692,709.32
  5. Step 5: Solve for x
    x = 692,709.32/1,109.53
  6. Step 6: Final answer
    x = 624.33

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.